Consumers would vote with their feet and switch current accounts if their bank started to charge for its services, research shows.
Eight out of 10 people say they would consider moving if their bank introduced annual or monthly fees for their current account, according to a survey by consumer group Which?
It comes amid a consumer revolt on current account and credit card charges that is costing the industry billions.
The Office of Fair Trading is currently investigating banks' pricing structures in a wide-ranging study that is due to be published by the end of the year.
It has already forced providers to cut credit card default charges to 12 pounds or less, and industry commentators have said a wider crackdown on charges could herald an end to free banking as companies try to recoup lost revenue.
However, 73 percent of 1,022 people surveyed by Which? believe additional fees would be unfair at current service levels.
If banks were to introduce fees, 87 percent think the government should intervene to ensure they are not excessive.
Doug Taylor, a spokesman for Which?, said the findings were a clear shot across the bows for the banks.
Banks shouldn't need to be forced to treat their customers fairly, he added.
Banks only have themselves to blame for the damage that the overdraft charges saga has done to their reputation. Which? urges the banking sector to put its customers first.